Mathematics Course Descriptions

MATHEMATICS DEPARTMENT

    

ALGEBRA I 10                                                                                              2.50 Credits/Semester

Course #301

This honors-level college preparatory course will provide a rigorous study of traditional algebra topics from the Common Core State Standards including, solving equations and inequalities, graphing and solving both linear and quadratic equations, solving systems of equations, properties of exponents, working with polynomials and factoring, and operations with rational expressions. This course is designed to build on students’ prior understanding of Algebra and to develop the solid foundation needed to succeed at the honors level throughout the high school math curriculum.

Prerequisite: This course is open to students who have completed Algebra 10 at the middle school level and would like to strengthen their understanding of algebra. It is also open to students who earned a grade of A or better in the 8th grade Math Program or with the permission of the head of the NHS Math Department.


 

ALGEBRA I 11                                                                                              2.50 Credits/Semester

Course #303

This advanced college preparatory course is designed to provide a solid foundation of algebra following the Common Core State Standards for the college-bound student. The goals of Algebra 11 are to provide opportunities for students to learn about solving and graphing linear and quadratic equations, solving algebraic equations, solving systems of equations and inequalities, exponents, and operations with rational numbers. The curriculum largely parallels that of Algebra 10 without a review at the start of the year and with a somewhat less rigorous level of in-depth study in some areas.

Prerequisite: This course is recommended for students who participated in the 8th Grade Math Program and for those who took Algebra I in 8th grade and would like to strengthen their understanding of Algebra.

 

GEOMETRY 20                                                                                            2.50 Credits/Semester

Course #315

The objective of this rigorous honors college preparatory course is for students to develop an understanding of the mathematics of spatial forms and how this branch of mathematics lends itself to the art of reasoning. It places considerable emphasis on fundamental principles of logic and the role they play in the inductive and deductive processes. Following the Common Core State Standards, students will develop basic definitions, postulates and theorems are critically examined and subsequently applied to a detailed study of angles, triangles, quadrilaterals, perpendicularity and parallelism.  Students will study right triangle trigonometry. Although mastery of concepts in two- dimensional geometry is the primary goal of the course, three-dimensional concepts are also introduced.

Prerequisite: Students must have earned a grade of B- or better in Algebra I (10) or a grade of A- or better in Algebra I (11), or receive the permission of the head of the NHS Math Department.

 

GEOMETRY 21                                                                                            2.50 Credits/Semester

Course #317

This advanced college preparatory course will largely parallel the topics of the Geometry 20 course, with somewhat less emphasis on the theoretical aspects of geometry. Following the Common Core State Standards, topics to be explored include inductive and deductive reasoning, properties of triangles and special right triangles, polygons, circles, area, volume, and similarity. Students will learn to apply these concepts to numerous real-world models. Students will explore right triangle trigonometry, proof and construction of geometric figures using a variety of manual and technological tools.

Prerequisite: Students must have completed Algebra 10 or earned a grade of C- or better in Algebra 11.


 

GEOMETRY 22                                                                                            2.50 Credits/Semester

Course #319

A major goal of this college preparatory course is to develop an understanding of the concepts of geometry following the Common Core State Standards. Topics to be explored include inductive and deductive reasoning, proofs, properties of triangles and special right triangles, polygons, circles, area, volume, and similarity. One objective that is stressed is the development of the student’s ability to think logically and deductively. Students will explore concepts including right triangle trigonometry, proof and geometric constructions.  This course will include a substantial focus on the topics often covered on the 10th grade MCAS mathematics examination.

Prerequisite: Generally, students must have completed Algebra I. Sophomores who have not completed Algebra I may take this course and Algebra I concurrently.

 

ALGEBRA II 30                                                                                             2.50 Credits/Semester

Course #321

This honors-level college preparatory course is intended for students who are capable of profiting from an accelerated and deeper treatment of the topics of an Algebra II-Trigonometry course in one year. Following the Common Core State Standards, topics will include properties and operations in the real number system, sequences and series, graphing and solving quadratic equations, systems of equations, matrices, functions, graphing first- and second-degree equations and trigonometry. Students will learn to solve a wide range of problems using a graphing calculator.

Prerequisite: Students must have completed Geometry 20 with a grade of B- or better, completed Geometry 21 with an A- or better, or received permission of the Math Department Head.

 

ALGEBRA II 31                                                                                             2.50 Credits/Semester

Course #323

This advanced college preparatory course is designed to build on students’ existing mathematical skills and help them develop more sophisticated problem-solving skills. This course is important for success on the SAT and in subsequent mathematics courses. Following the Common Core State Standards, topics include: properties and operations throughout the real number system, sequences and series, graphing and solving quadratic equations, systems of equations, functions, graphing first- and second-degree equations and the elements of coordinate geometry. Students will learn to solve a wide range of problems using a graphing calculator.

Prerequisite: This course is for students who have completed Geometry 20, or have received a grade of B- or better in Geometry 21, or have completed Geometry 22 with a grade of A- or better.

 

ALGEBRA II 32                                                                                             2.50 Credits/Semester

Course #325

In this college preparatory course, students will develop their ability to think logically and refine their mathematical skills to prepare themselves for the SAT, future courses involving mathematics, and the application of these concepts in the real world. Following the Common Core State Standards, topics of discussion include real numbers and integers, polynomials and factoring, sequences and series, rational expressions, irrational numbers, simple radical expressions, exponents and quadratic equations. This course focuses on problem solving strategies and real world application of mathematics. In this course students will learn to use a graphing calculator to solve a variety of problems.

Prerequisite: This course is for students who have completed Geometry.


 

PRE-CALCULUS 40                                                                         2.50 Credits/Semester

Course #333

This rigorous honors-level college preparatory course enables mathematically sophisticated students to expand upon, integrate, and develop strong theoretical mathematical skills. It forms the basis for a solid course in calculus and helps prepare students for the mathematics found in a variety of other disciplines. Following the Common Core State Standards, the topics investigated are: trigonometric functions and analytic trigonometry, theory of polynomial functions, rational and power functions, complex numbers, exponential and logarithmic functions, the mathematics of finance and topics in discrete mathematics such as mathematical induction, sequences and series, and combinatorics. Throughout the year, students will apply the mathematical concepts they learn to a variety of mathematical models and real world problems.

Prerequisite: Students must have completed Algebra II (30) with a grade of B- or better or completed Algebra II 31 with a grade of A- or better and completed additional work in the area of trigonometry.

 

PRE-CALCULUS 41                                                                         2.50 Credits/Semester

Course #335

This advanced college preparatory course prepares students for future studies in calculus and other college-level mathematics courses. Curriculum will follow the Common Core State Standards. Approximately half of the course will be devoted to study of trigonometry. The other half of the course will explore topics in discrete mathematics and functions, including polynomial functions, rational functions, and exponential and logarithmic functions. Throughout the year, this course will include an emphasis on the real-world applications of the topics discussed.

Prerequisite: Students must have completed Algebra II (30), or completed Algebra II (31) with a grade of C- or better or completed Algebra II (32) with a grade of A- or better.

 

ADVANCED ALGEBRA 42                                                             2.50 Credits/Semester

Course #326

This year-long college preparatory course prepares students for future studies in mathematics and prepare students for standardized tests including the SAT, ACT and Accuplacer. Topics include functions and linear equations, systems of equations and matrices, exponents and polynomial functions, rational expressions, roots and radical functions, quadratics, inverse, exponential and logarithmic functions and trigonometry.  Throughout the year, this course will explore real-world applications of the topics discussed.  Students may not take this course after completing Precalculus 40 or 41. 

Prerequisite: Students must have completed Algebra II (30).

 

PROBABILITY AND STATISTICS 41/42                                                2.50 Credits/Semester

Course 361, 362

This year-long college preparatory course prepares students for future studies in statistics and other college-level courses that make use of statistics.   During the first semester, the course will be explore key terms, categorical and quantitative variables, populations, samples, various representations of data, frequency, independent and dependent variables, contingency, standard deviation, normal distribution, outliers, percentiles, scatterplots, correlations and gathering data.   The second semester will focus on randomness, probability, combinations, permutations, binomial probabilities, confidence intervals, and inference.  Throughout the year, this course will include an emphasis on the real-world applications of the topics discussed.

Prerequisite: Students must have completed Algebra II.  Preference in enrollment will be given to seniors.

 

                                                                                    2.50 Credits/Semester

 

AP CALCULUS AB 50                                                                                 2.50 Credits/Semester

Course #329

This Advanced Placement course is designed to prepare students to succeed on the Advanced Placement Calculus AB examination. Students will study differential and integral calculus, two of the most powerful tools in mathematics. This course follows topics outlined by the College Board and is designed to prepare students for the Calculus AB Advanced Placement Examination. Students are challenged to strengthen and build on their mathematical skills and to pursue diverse problem situations with clarity, conviction, and enthusiasm.

Prerequisite: This course is open to students who have completed Pre-Calculus (40) with a B+ or better, or with the approval of the Math Department Head.

 

AP CALCULUS BC 50                                                                                 2.50 Credits/Semester

Course #331

This Advanced Placement course is designed for those exceptional math students who intend to pursue further study in mathematics, science or engineering. The course, which follows the topics outlined by the College Board, will prepare students to succeed on the Advance Placement Calculus BC examination. Students will cover all of the topics covered in the AB Calculus course, including differential and integral calculus, and will explore additional topics including infinite series, and parametric, vector, and polar functions. This will be a fast paced course, taught with the expectation that students understand and can apply those topics learned in Pre-Calculus without further review.

Prerequisites: This course is open to students who have completed Pre-Calculus (40) with an A or better, or with the approval of the Math Department Head.

 

AP COMPUTER SCIENCE 30                                                                    2.50 Credits/Semester

Course #341

This challenging full-year course is designed to prepare students to succeed on the Advanced Placement Computer Science Course, which is based in the JAVA programming language. The curriculum is based on the College Board’s recommended topics of study, including: an introduction to JAVA, classes of variables, input and output techniques, logical operators, if statements, nested loops, arrays and recursion. An emphasis will be placed on effective programming design, testing and debugging strategies. Approximately half of the course will be lecture and discussion, while half will be hands-on programming.

Prerequisite: Students must have a grade of B- or better in Algebra II (30, 31) or permission of the Mathematics Department Head.

 

AP STATISTICS 30                                                                                     2.50 Credits/Semester

Course #343

This is a rigorous full-year Advanced Placement course that is equivalent to a college-level statistics course. Students are strongly encouraged to take the AP Statistics Exam, and if successful may be eligible to receive college credit. The course content is divided into four categories as follows: exploratory analysis of data which makes use of graphical and numerical techniques to study patterns and departure from patterns, collection of data according to well-developed plans in order to obtain valid information on a conjecture, use of probability to anticipate what the distribution of data should look like under a given model, and statistical inference which guides the selection of appropriate models.

Prerequisite: Students must have completed Algebra II (30) with a grade of B- or better, or completed Algebra 31 with a grade of A- or better, or have the approval of the Math Department Head.

 

MULTIVARIABLE CALCULUS 50                                                 2.50 Credits/Semester

Course #334

This honors-level course will explore those concepts in calculus that follow those covered in AP Calculus (B/C), as generally occurs at most universities. Moving beyond the concept of the two-dimensional x,y plane, students will learn how to work with mathematics in a third dimension. We will learn the calculus of this x,y,z space and apply this math to solve real-world problems.

Prerequisite: AP Calculus BC and permission of the Mathematics Department Head

 

HONORS CALCULUS 50                                                                           2.50 Credits/Semester

Course #345

In this honors college preparatory course, students will build on the concepts learned in Pre-Calculus, learning about limits, differentiation, and integration. Students will apply these concepts to a wide range of real-world problems, including rates of change, optimization, and velocity/acceleration.   This course will use many of the same materials as the A.P. Calculus courses.

Prerequisite: Grade of B- or better in Honors Pre-Calculus, a grade of A- or better in Pre-Calculus 41, or permission of the math department head.

 

INTRODUCTION TO CALCULUS 51                                                      2.50 Credits/Semester

Course #339

In this college preparatory course, students will build on the concepts learned in Pre-Calculus, learning about limits, differentiation, and integration. Students will apply these concepts to a wide range of real-world problems, including rates of change, optimization, and velocity/acceleration.  This course will include a review of key precalculus topics (not given in the other Calculus courses) and will include a substantial focus on applications of calculus.  This course will provide a solid foundation for students planning on studying mathematics-related topics in college. This course will be of particular interest to students who wish to prepare themselves for the use of mathematics in business, economics, and the sciences.

Prerequisite: Completion of Honors Precalculus, a grade of C- or better in Pre-Calculus 41, or permission of the math department head

 

INTRODUCTION TO COMPUTER SCIENCE   21                                2.50 Credits/Semester

Course 340a, 340b

This semester-length course will be offered both semesters.  In this course students will be exposed to multiple aspects of programming.  They will learn the logic of programming, write programs, and gain an introductory understanding of the software that underlies many applications we commonly use.  Class time will be divided approximately evenly between instruction/discussion and hands-on writing of code.

Prerequisite – Completion of Algebra I.


 

HONORS ACCOUNTING 30                                                                    2.50 Credits/Semester

Course #373

The College Board is developing an Advanced Placement Accounting Course and Exam.  This course will follow the syllabus for that developing course.  This first semester of this rigorous year-long college preparatory course focuses on the relationships between business activities and events and the impact they have on financial statements (financial accounting).  Students study financial transactions and relate the transactions to a company's assets, liabilities, owner's equity, revenue, expenses, and cash flow. Areas of study include the basic accounting cycle, accounting principles and terminology, financial statement analysis, and a computerized general ledger system.  The second semester of the course examines information that will be useful to managers and executives in such functions as planning and controlling operations of a business (managerial accounting). Topics include profit analysis, decision-making, budgeting, forecasting and financial statement analysis. Students learn to use and interpret accounting data as the basis for managerial decision-making and planning.  This course parallels Accounting 21, but moves at a substantially faster pace and has a more workload.

Prerequisite – Completion of Algebra 30 with a grade of B- or better, completion of Algebra 31 with an A- or better.

 

ACCOUNTING 21                                                               2.50 Credits/Semester

Course #373

This first semester of this year-long college preparatory course focuses on the relationships between business activities and events and the impact they have on financial statements (financial accounting) . Students study financial transactions and relate the transactions to a company's assets, liabilities, owner's equity, revenue, expenses, and cash flow. Areas of study include the basic accounting cycle, accounting principles and terminology, financial statement analysis, and a computerized general ledger system.  The second semester of the course examines information that will be useful to managers and executives in such functions as planning and controlling operations of a business (managerial accounting). Topics include profit analysis, decision-making, budgeting, forecasting and financial statement analysis. Students learn to use and interpret accounting data as the basis for managerial decision-making and planning.

 

ENTREPRENEURSHIP 31                                                                           2.50 Credits/Semester

Course #376a, 376b

This one semester advanced college preparatory course is designed to introduce students to the world of business. Concepts will include finance, management (business and human resources), business organization, ethics, etc. Each student will be expected to prepare a project in which they choose, finance and establish a single owner business.

Prerequisite: Juniors and Seniors only.

 

FINANCIAL LITERACY 31                                                                         2.50 Credits/Semester

Course #375a, 375b

This is a one semester advanced college preparatory course that will introduce students to the very important role of personal money management. Topics will include preparation of a budget, saving and checking products, credit cards, loans, and apartment leases, “homework” necessary before purchasing major products, preparation for life changes and for retirement. This course is designed to provide each student with basic and necessary life skills.

Prerequisite: Juniors and Seniors only.

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